Question

kindly find the solution with the steps

Answer 1

Answer:

Answer is A) 14

Step-by-step explanation:

x = 2 - √3

Formulas used:

$(a - b {)}^{2} = {a}^{2} + {b}^{2} - 2ab$

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

PROBLEM

${x}^{2} = 4 + 3 - 4√3 = 7 - 4√3$

${x}^{2} + \frac{1}{ {x}^{2} } = \frac{49 + 48 - 56 \sqrt{3} + 1}{7 - 4 \sqrt{3} }$

$\frac{(98 - 56 \sqrt{3} )(7 + 4 \sqrt{3)} }{(7 - 4 \sqrt{ 3})(7 + 4 \sqrt{3} ) }$

$\frac{686 + 392 \sqrt{3} - 392 \sqrt{3} - 672 }{1} = 14$

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